Uncertainty Contribution Table for Balances
Contribution (nomenclature)Distribution
us Uncertainty of the Normal
nominal values of the
reference weight set
sp Standard deviation of
the set of calibration
Normal
readings
u1 Standard uncertainty
associated with the
Uniform
(Square)
repeatability of the
balance response to
the reference weight
set.
Uncertainty Contribution Table for Thermometers
Contribution (nomenclature)Distribution
ur Standard uncertainty Normal
of the nominal values
of the reference
thermometer.
sp Standard deviation of
the set of calibration
Normal
readings
u1 Standard uncertainty
of the readability and
Uniform
(Square)
resolution of the
working thermometer
Uncertainty Contribution Table for Pipettes
Contribution Distributi
(nomenclature) on
ur Standard uncertainty Normal
of the nominal values
of the reference
balance.
sp Standard deviation of
the set of calibration
Normal
readings deviation of
sT Standard
corrections caused by
Uniform
(Square)
temperature (∆T) when
the temperature differs
from standard
temperature (20oC).
The thermal coefficient
of expansion of water
is 0.00021 per 1°
Celsius at 20° Celsius.
u1 Standard uncertainty
of the readability and
Uniform
(Square)
resolution of the
working volumetric
instrument
on Table for Balances
Estimated Value (NISTIR 6919)
Expanded uncertainty on
the calibration certificate
of the weights divided by 2
(coverage factor – k)
Standard deviation of the
set of calibration
measurements.
Smallest display increment
divided by √3 if unable to
determine from 7
consecutive readings. Use
ONLY if Sp = 0.
Table for Thermometers
Estimated Value
Expanded uncertainty on
the calibration certificate
of the reference
thermometer divided by 2
(coverage factor – k)
Standard deviation of the
set of calibration
measurements.
Smallest gradation of the
working thermometer
divided by √3. Use ONLY
if Sp = 0
on Table for Pipettes
Estimated Value
Expanded uncertainty on
the calibration certificate
of the reference balance
divided by 2 (coverage
factor – k)
Standard deviation of the
set of calibration
measurements.
Relative Standard
Deviation = (∆T x 0.0002) /
(√3) in millilitres per
millilitre
Smallest gradation of the
working volumetric
instrument divided by √3.
Use ONLY if Sp = 0
Balance Calibration Worksheet
Model Serial / Lab
number MN07 number
Ref Mass (grams) 0.01 SN000124
Smallest
Working Balance: B534 Display
Increment
Analyst/TechnicianJane Doe
Balance Readings (grams) Date:
No. Unloaded Loaded |Diff| |Diff – Mean|
1 0.000 0.010 0.010 -
2 0.000 0.010 0.010 -
3 0.000 0.010 0.010 -
4 0.000 0.011 0.011 0.0010
5 0.000 0.010 0.010 -
6 0.000 0.009 0.009 0.0010
7 0.000 0.010 0.010 -
n=7 Sum diff 0.070 Sum squares
us = ### Mean: 0.010 Std Dev: sp
Combined Standard Uncertainty
uc = √ (us)2 + (sp)2+ (u1)2
Expanded Uncertainty
k=2 U = k (uc) for smallest mass
Balance Calibration Worksheet
Model Serial / Lab
number MN09 number
Ref Mass (grams) 10
Workin SN77
Smallest
g
T534 Display
Balance
Increment
:Analyst/TechnicianJane Doe
Balance Readings (grams) Date:
No. Unloaded Loaded |Diff| |Diff – Mean|
1 0.000 10.000 10.00 0.000
2 0.000 10.001 10.00 0.001
3 0.000 10.000 10.00 0.000
4 0.000 9.999 10.00 0.001
5 0.000 10.000 10.00 0.000
6 0.000 10.001 10.00 0.001
7 0.000 10.000 10.00 0.000
n=7 Sum diff 70.00 Sum squares
us = ### Mean: 10.00 Std Dev: sp
Combined Standard Uncertainty
uc = √ (us)2 + (sp)2+ (u1)2
Expanded Uncertainty
k=2 U = k (uc) for middle mass
Balance Calibration Worksheet
Model Serial / Lab
number MN88 number
Ref Mass (grams) 50 SN654
Smallest
Working Balance: T534 Display
Increment
Analyst/TechnicianJane Doe
Balance Readings (grams) Date:
No. Unloaded Loaded Diff |Diff – Mean|
1 0.00 50.01 50.01 0.009
2 0.00 49.99 49.99 0.011
3 0.00 50.00 50.00 0.001
4 0.00 49.99 49.99 0.011
5 0.00 50.00 50.00 0.001
6 0.00 50.01 50.01 0.009
7 0.00 50.01 50.01 0.009
n=7 Sum diff ### Sum squares
us = 0.0001 Mean: 50.00 Std Dev: sp
Combined Standard Uncertainty
uc = √ (us)2 + (sp)2+ (u1)2
Expanded Uncertainty
k=2 U = k (uc) for greatest mass
Smallest Weight
0.001
9-Nov-09
(|Diff – Mean|)2
-
-
-
0.0000010
-
0.0000010
-
0.0000020
0.0005774
0.0005774
0.0012
Middle Weight
0.001
9-Nov-09
(|Diff – Mean|)2
0.000000
0.000001
0.000000
0.000001
0.000000
0.000001
0.000000
0.000003
0.000282
0.000282
0.0006
Heaviest Weight
0.01
9-Nov-09
(|Diff – Mean|)2
0.00007
0.00013
0.00000
0.00013
0.00000
0.00007
0.00007
0.00049
0.00367
0.00367
0.00735
Thermometer Calibration Worksheet
Model Serial / Lab
number MN02 number
Ref ThermometerT01 SN000123
Working Thermometer: T29 Smallest Gradat
Analyst/Technician Jane Doe
Thermometer Readings (0C) Date:
No. ReferenceWorking Diff |Diff – Mean|
1 4.07 4.0 0.07 0.0157
2 4.05 4.0 0.05 0.0043
3 4.00 4.0 0.00 0.0543
4 4.02 4.0 0.02 0.0343
5 4.05 4.0 0.05 0.0043
6 4.09 4.0 0.09 0.0357
7 4.10 4.0 0.10 0.0457
n=7 Sum d: 0.380 Sum s:
ur = 0.03 Mean: 0.054 Std Dev: sp
Combined Standard Uncertainty
uc = √ (ur)2 + (sp)2+ (u1)2
Expanded Uncertainty
k=2 U = k (uc)
CLARIFICATION AND CORRECTION NOTE:
ur was changed to a value more representative of a reference thermometer. This changed the values for combined and
standard uncertainty.
0.5
10-Nov-09
(|Diff – Mean|)2
0.0002
0.0000
0.0029
0.0012
0.0000
0.0013
0.0021
0.0078
0.0360
0.0469
0.09
anged the values for combined and
Pipette Calibration Worksheet
Identification Model number
Ref Balance B01 MN332
Pipette P002
Analyst/Technician Jane Doe
Temperature in degrees Celci 24 Temperature Correction cont
Nominal Dispensed Volume (m 1 Evap Loss Corr in millilit
Pipette and Balance Readings (mg, g, µl, ml, etc)
No. Balance Nominal Corrected
Mass (g) Vol (ml) Vol (ml) Vol (ml)
1 1.0000 1.0000 1.00 0.9875
2 1.9905 1.9905 2.00 1.9871
3 2.9810 2.9810 3.00 2.9866
4 3.9704 3.9704 4.00 3.9862
5 4.9706 4.9706 5.00 4.9857
6 5.9600 5.9600 6.00 5.9852
7 6.9404 6.9404 7.00 6.9848
8 7.9300 7.9300 8.00 7.9843
9 8.9103 8.9103 9.00 8.9838
10 9.9080 9.9080 10.00 9.9834
n=10 Sum d:
ur = 0.0007 Mean:
Standard Uncertainty of this dispensed volume
uc = √ (ur)2 + (sp)2+ (sT)2 + (u1)2
Expanded Uncertainty
U = k (uc), k = 2
CLARIFICATION AND CORRECTION NOTE:
Please note that the value in Cell H8 is an experimental evaporation rate (in mL for 30 seconds) determined by
liquid being dispensed under the laboratory conditions used for the pipette calibration (loss measured after 30
worksheet presents example data for 1 mL under the conditions used by the laboratory for pipette calibrations.
experimentally determined by the laboratory for each volume being dispensed (calibrated) under the lab condi
pipetted, the correction may be negligible. The actual correction factor applied in Cell H9 (Cell H8 divided by fi
time (6 seconds) required for the balance to stabilize following the dispensing of each aliquot for weighing.
Please note that a minor error in the spreadsheet has been corrected. This error did not significantly affect unc
calibrations conditions greatly vary from 20 C. The temperature correction in cell H7 should not be an absolute
The formula has been corrected in this version of the spreadsheet to remove the absolute value function.
To facilitate understanding of calculations, table values have been expanded to 4 decimal places as would be e
balance.
alibration Worksheet
Serial / Lab number
SN00099387
Smallest Disp Vol 0.10
Date: 23-Oct-09
mperature Correction contribution in ml 0.0005
ap Loss Corr in millilit(at 30 seconds) 0.0600
ml, etc) (per reading) 0.0120
Diff (Bal – Corr) |Diff – Mean| |(Diff - Mean)|^2
Vol (ml) Vol (ml) Vol (ml)
(0.0125) 0.0418 0.0017
(0.0034) 0.0328 0.0011
0.0056 0.0237 0.0006
0.0158 0.0136 0.0002
0.0151 0.0142 0.0002
0.0252 0.0041 0.0000
0.0444 0.0150 0.0002
0.0543 0.0250 0.0006
0.0735 0.0442 0.0020
0.0754 0.0460 0.0021
0.2934 Sum s: 0.0087
0.0293 sp = Std Dev 0.0311
0.03
0.06
rate (in mL for 30 seconds) determined by the laboratory for the specific volume of
pipette calibration (loss measured after 30 seconds). It is not a percentage. This
d by the laboratory for pipette calibrations. The evaporation rate needs to be
dispensed (calibrated) under the lab conditions. Depending on conditions and volume
ctor applied in Cell H9 (Cell H8 divided by five) represents the evaporation in the typical
ispensing of each aliquot for weighing.
d. This error did not significantly affect uncertainty, but may affect a bias calculation if
rection in cell H7 should not be an absolute value.
o remove the absolute value function.
xpanded to 4 decimal places as would be expected when using a 4-place analytical
